1.5.4 Traveling Salesman Problem

INPUT OUTPUT

Input Description:
A weighted graph G.

Problem:
Find the cycle of minimum cost visiting all of the vertices
of G exactly once.

Excerpt from
The Algorithm Design Manual:
The traveling salesman problem is the most notorious NP-complete problem.
This is a function of its general usefulness, and because
it is easy to explain to the public at large.
Imagine a traveling salesman who has to visit each of a given set of cities
by car.

Although the problem arises in transportation applications, its most
important applications arise in optimizing the tool paths
for manufacturing equipment.
For example, consider a robot arm assigned to solder all the connections on
a printed circuit board.
The shortest tour that visits
each solder point exactly once defines the most efficient path for the robot.
A similar application arises in minimizing the amount of time taken by
a graphics plotter to draw
a given figure.